Theorems · Theorem · linear algebra
Matrix.charpoly_sub_scalar
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (M : Matrix n n R)
(μ : R), (M - (Matrix.scalar n) μ).charpoly = M.charpoly.comp (Polynomial.X + Polynomial.C μ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Unitsproof · cited by 2,804
- Finset.prodproof · cited by 2,356
- Finset.sum_congrproof · cited by 2,323
- Polynomial.Xstatement and proof · cited by 1,639
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_sub_smulproof · cited by 2